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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nondegeneracy of entire solutions of a singular Liouvillle equation


Authors: Manuel del Pino, Pierpaolo Esposito and Monica Musso
Journal: Proc. Amer. Math. Soc. 140 (2012), 581-588
MSC (2010): Primary 35J25, 35B40, 35J10
Published electronically: July 20, 2011
MathSciNet review: 2846326
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Abstract: We establish nondegeneracy of the explicit family of finite mass solutions of the Liouvillle equation with a singular source of integer multiplicity, in the sense that all bounded elements in the kernel of the linearization correspond to variations along the parameters of the family.


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Additional Information

Manuel del Pino
Affiliation: Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (UMI 2807 CNRS), Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Email: delpino@dim.uchile.cl

Pierpaolo Esposito
Affiliation: Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo S. Leonardo Murialdo, 1, 00146 Roma, Italy
Email: esposito@mat.uniroma3.it

Monica Musso
Affiliation: Departamento de Matemática, Pontificia Universidad Católica de Chile, Avda, Vicuña Mackenna 4860, Macul, Chile
Email: mmusso@mat.puc.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11134-1
PII: S 0002-9939(2011)11134-1
Keywords: Singular Liouville equation, linearization, nondegeneracy
Received by editor(s): November 23, 2010
Published electronically: July 20, 2011
Additional Notes: This research has been partly supported by grants FIRB-IDEAS (2008), project “Geometrical aspects in PDEs”, Fondecyt Grants 1070389, 1080099, Fondo Basal CMM and CAPDE-Anillo ACT-125.
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2011 American Mathematical Society